In a parallel plate capacitor, the distance between the plates is d and potential difference across the plates is V. Energy stored per unit volume between the plates of capacitor is ?

In a parallel plate capacitor, the distance between the plates is d and potential difference across the plates is V. Energy stored per unit volume between the plates of capacitor is ?

(a) \( \frac{Q^2}{2V^2} \)

(b) \( \frac{1}{2} \varepsilon_0 \frac{V^2}{d^2} \)

(c) \( \frac{1}{2} V^2 \varepsilon_0 d^2 \)

(d) \( \frac{1}{2} \varepsilon_0 \frac{V^2}{d} \)

Answer :  (b) \( \frac{1}{2} \varepsilon_0 \frac{V^2}{d^2} \)

\( \frac{U}{\text{vol.}} = \frac{\frac{1}{2} C V^2}{A \cdot d} \)

\( = \frac{1}{2} \cdot \frac{\varepsilon_0 A}{d} \cdot \frac{V^2}{A \cdot d} \)